Forming method for milling threads of variable tooth worms

ABSTRACT

A forming method for milling teeth of variable tooth worms (VTW) with the following features: on a multi-axis simultaneously-working CNC machine-tool a moving coordinate system {σ 1 (φ 1 )[O 1 ;{right arrow over (i)} 1 (φ 1 ),{right arrow over (j)} 1 (φ 1 ),{right arrow over (k)} 1  (φ 1 )]} is correlated to the worm blank of the VTW worms, whereon the worm blank of the VTW worms rotates around {right arrow over (k)} 1 (φ 1 )-axis at angular speed |{right arrow over (ω)} 1 |; another moving coordinate system {σ 2 (φ 2 )[O 2 ; {right arrow over (i)} 2 (φ 2 ), {right arrow over (j)} 2 (φ 2 ), {right arrow over (k)} 2 (φ 2 )]} is correlated to the milling cutter, whereon the milling-cutter rotates around {right arrow over (k)} 2 (φ 2 )-axis at angular speed |{right arrow over (ω)} 2 |, |{right arrow over (ω)} 1 |/|{right arrow over (ω)} 2 |=i 12  and i 12  is a constant; the feed motion of the milling cutter comprises the radial shift along {right arrow over (i)} 2 (o 2 )-axis and the peripheral shift around {right arrow over (k)} 2 (φ 2 )-axis; the equations of the cutting edge of the milling cutter are given as below
 
x=u
 
 y   2   =r   b   −v  sin β
 
 z   2   =v  cos β.

CROSS REFERENCE TO RELATED APPLICATION

This application is a continuation-in-part application of applicationSer. No. 09/978,340 now abandoned, filed Oct. 17, 2001, entitled “METHODOF FORMING MILLED TOOTH OF VARIABLE TOOTH WORM”.

FIELD OF THE INVENTION

This invention relates to a forming method for milling the threads ofcylindrical variable tooth worms.

BACKGROUND OF THE INVENTION

The worm transmissions may be classified into two sorts: the first sortis a cylindrical worm transmission; the second one is a toroidal wormtransmission. While the cylindrical worms can further be classified intoan involute helicoid worm (ZI for short, the same hereinafter), anArchimedes worm (ZA), a milled helicoid worm (ZK), and a variable toothworm (VTW) disclosed in China patent No. ZL96244108.2 and U.S. Pat. No.6,176,148B1 with accordance to the different profile thereof. The wormsof ZI-, ZA- and ZK-type can all be formed by lathing withdifferent-profile cutters. However, the relationship of the relativemovement between the workpiece and the cutter is the same.Alternatively, the different types of worms such as ZI, ZA and ZK can bemachined on the same machine tool with the worm blank turning and thecutter feeding along the longitudinal and radial directions relativelyto the worm blank, the one thing must be done only is to change thecorresponding cutter. Although the variable tooth worm (VTW) isclassified into the cylindrical worms, they cannot be machined on thesame facilities with the existing motion relationship even if the cutterwere changed seeing that the tooth thickness of the variable tooth wormsis changeable along either longitudinal or tooth height direction. Theminimum tooth thickness of the worms is at the gorge part of the thread,while it gradually thickens toward both ends, as shown in the FIGS. 1and 2.

The worms patented as disclosed in U.S. Pat. No. 1,853,643 with thetitle of “METHOD OF AND APPARATUS FOR GENERATING THE CONVOLUTE TEETH ORTHREADS OF WORMS AND THE LIKE” (hereinafter referred to as Simmonspatent) are machined by using a gear-shape cutter. The profile of thecutting edges of the gear shaped cutter for machining the thread ofworms in Simmons patent is an involute in the end face. Let the radiusof the basic cylindroid of the gear shaped cutter be r_(b), theintersected line of tangential plane Σ with the side surface of thecutter tooth is a straight line as shown in the FIG. 3. Therefore,Simmons method for forming the involute worms can not be used forforming the thread of variable tooth worms with a circular toroid, or anelliptic toroid, or a parabolic toroid.

SUMMARY OF THE INVENTION

The object of the present invention is to supplement the deficiency ofthe existing technology and to provide a forming method for milling thethread of variable tooth worms with high productivity and high machiningaccuracy.

In order to realize the object, the following technical solution will beadopted. A moving coordinate system {σ₁(φ₁)[O₁; {right arrow over (i)}₁(φ₁), {right arrow over (j)}₁ (φ₁), {right arrow over (k)}₁(φ₁)]} iscorrelated to the worm blank of variable tooth worms and the worm blankrotates about {right arrow over (k)}₁(φ₁)-axis at angular speed {rightarrow over (ω)}₁; A moving coordinate system {σ₂(φ₂)[O₂; {right arrowover (i)}₂ (φ₂), {right arrow over (j)}₂(φ₂), {right arrow over(k)}₂(φ₂)]} is correlated to the milling cutter and the cutter rotatesabout {right arrow over (k)}₂(φ₂)-axis at angular speed {right arrowover (ω)}₂, whereof |{right arrow over (ω)}₁|/|{right arrow over(ω)}₂|=i₁₂, i₁₂ is a constant. The feeding movement of the millingcutter is composed by two components: one component is the radial shiftalong the {right arrow over (i)}₂(o₂)-axis; another the peripheral shiftaround {right arrow over (k)}₂(φ₂)-axis. The equations of the cuttingedge of the milling cutter are given as below.x=uy ₂ =r _(b) −v sin βz ₂ =v cos βWhere, u,v are the parameters of the generatrix plane of variable toothworm; β is the inclination angle of the generatrix plane; r_(b) is theradius of the main basic circle of the cutter body; x₂, y₂, z₂ are thecoordinate values of the generatrix plane.

The advantages and the effect of this invention show that the machiningmethod of this invention has higher productivity, more powerful cuttingforce, less machining hours and reaches higher machining accuracy ascompared with other machining method for any cylindrical worm by meansof a spatial cutter that has multiple blades thereon, therefore thereare multiple edges simultaneously to take part in cutting the VTW wormblank.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1 and 2 are the schematic views showing the VTW worm and thecoordinate system of the prior art of China patent No. ZL96244108.2(U.S. Pat. No. 6,176,148B1).

FIG. 3 is a schematic view showing the profile of the cutting edges ofthe gear shaped cutter of U.S. Pat. No. 1,853,643.

FIG. 4 is a schematic view showing the relationship between an imaginarycone and a generatrix plane thereof and a coordinate system {σ₂(φ₂)[O₂;{right arrow over (i)}₂ (φ₂), {right arrow over (j)}₂ (φ₂), {right arrowover (k)}₂(φ₂)]} according the principle of the invention.

FIG. 5 is a schematic view showing the relationship between disc-shapedcutter and a coordinate system {σ₂(φ₂)[O₂; {right arrow over (i)}₂ (φ₂),{right arrow over (j)}₂ (φ₂), {right arrow over (k)}₂(φ₁)]} accordingthe principle of the invention.

FIG. 6 is a schematic view further showing the relationship betweendisc-shaped cutter and a coordinate system {σ₂(φ₂)[O₂; {right arrow over(i)}₂ (φ₂), {right arrow over (j)}₂ (φ₂), {right arrow over (k)}₂(φ₂)]}according the principle of the invention.

FIG. 7 is a schematic view showing forming principle for the method offorming the variable worms according to the invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

By referring to the attached drawings and embodiments, the technicalscheme of the invention is further expounded as follows:

As shown in the FIGS. 4 and 7, an imaginary cone with the radius r_(b)of the main basic circle and the half conic angle β is correlated to thecoordinate system {σ₂(φ₂)[O₂; {right arrow over (i)}₂ (φ₂), {right arrowover (j)}₂ (φ₂), {right arrow over (k)}₂(φ₂)]}, and let a generatrixplane Σ be tangential to the cone at point o, the inclination angle ofthe plane Σ relative to k₂(φ₂)-axis be β, the parameters u and v areintroduced to express the characteristics of the plane Σ. In thisinvention the cutting edge of the disc-shaped cutter is disposed on thegeneratrix plane Σ described by u and v, and is tangential to thecircular cone expressed by r_(b) and β. It is not hard to be seen whatthe coordinate relationship among the cone and the tangential plan Σ aswell as a disc-shaped cutter is. The relationship between disc-shapedcutter and the coordinate system {σ₂(φ₂)[O₂; {right arrow over (i)}₂(φ₂), {right arrow over (j)}₂ (φ₂), {right arrow over (k)}₂(φ₂)]}, willbe further described, as jointly viewed with FIGS. 5 and 6.

As shown in the FIGS. 5 and 6, while the described disc-shaped cutterrotates about its own {right arrow over (k)}₂(φ₂)-axis, the generatrixplane Σ shall take the cutting edge thereon to rotate about {right arrowover (k)}₂(φ₂)-axis and keeps the tangential state with the cone frombeginning to end. The cutting edge of the disc-shaped cutter describedin this invention is disposed on the generatrix plane Σ as shown in theFIG. 6. When the generatrix plane Σ tangential to the cone rotates about{right arrow over (k)}₂(φ₂)-axis up to a position I, a row of thecutting edges are distributed on the generatrix plane Σ with theinclination angle β, while the generatrix plane Σ tangential to the conerotates about {right arrow over (k)}₂(φ₂)-axis up to another positionII, another row of the cutting edges are also on the generatrix plane Σ,the inclination angle of the generatrix plane Σ is still β. Themilling-cutter rotates around {right arrow over (k)}₂(φ₂)-axis atangular speed |{right arrow over (ω)}₂|, |{right arrow over(ω)}₁|/|{right arrow over (ω)}₂|=i₁₂ and i₁₂ is a constant; the feedmotion of the milling cutter comprises the radial shift along {rightarrow over (k)}₂(φ₂)-axis and the peripheral shift around {right arrowover (k)}₂(φ₂)-axis. The coordinate values of any point on the cuttingedge are all calculated according to the equations disclosed as follows:x=uy ₂ =r _(b) −v sin βz ₂ =v cos βWhere, u, v are the parameters of the generatrix plane of variable toothworm; β is the inclination angle of the generatrix plane; r_(b) is theradius of the main basic circle of the cutter body; x₂, y₂, z₂ are thecoordinate values of the cutting edge on the generatrix plane.

The method of this invention is illustrated in FIG. 7, showing therelative coordinate relationship between the worm-blank and the millingcutter in the coordinate systems according to the invention. Anothermoving coordinate system {σ₁(φ₁)[O₁; {right arrow over (i)}₁ (φ₁),{right arrow over (j)}₁ (φ₁), {right arrow over (k)}₁(φ₁)]} iscorrelated to the worm blank of the VTW worms, wherein the worm blank ofthe VTW worms rotates around {right arrow over (k)}₁(φ₁)-axis at angularspeed |{right arrow over (ω)}₁|, therefore shifting of cutting edge ofthe cutter on the cutter head according to the method of the inventionon the inclined generatrix plane in spatial locations is to envelop outand form the tooth flank of variable worms in the worm blank.

The detailed explanations of the method of this invention are given byfollowing preferred embodiments.

Embodiment 1:

On a five-simultaneously-working-axis CNC machine-tool, given that a VTWworm to be machined has β=18° the inclination angle of the generatrixplane, d₁=50.2 mm the reference diameter, and the center distancebetween the worm blank and the milling-cutter a=101.6 mm, themilling-cutter performs a cutting movement relatively to the worm blankwith the transmission ratio between the worm blank and the millingcutter i=41/4; the worm blank rotates around {right arrow over(k)}₁(φ₁)-axis at angular speed {right arrow over (ω)}₁, while themilling cutter rotates about {right arrow over (k)}₂(φ₂)-axis at angularspeed {right arrow over (ω)}₂ and simultaneously makes a radial feedalong {right arrow over (i)}₂(o₂)-axis and a peripheral feed around{right arrow over (k)}₂(φ₂)-axis. The radius of the main basic circle ofthe milling cutter r_(b)=33 mm and the coordinate values of the cuttingedge of the milling cutter are described according to the followingequationsx₂=u,y ₂ =r _(b) −v sin β,z ₂ =v cos β.Where,

-   -   u=64˜74    -   v=−24˜24    -   when u=70, v=−12, then    -   x₂=70 mm,    -   y₂=33−(−12×sin 18°)=36.708 mm,    -   z₂=−12×cos 18°=−11.413 mm.

All blades are fully mounted in three dimensions on the milling cutterbody and the cutting edges are all located at a spatial generatrixfamily.

Embodiment 2:

On a five-simultaneously-working-axis CNC machine-tool, given that a VTWworm to be machined has β=18° the inclination angle of the generatrixplane, d₁=50.2 mm the reference diameter, and the center distancebetween the worm blank and the milling-cutter a=101.6 mm, themilling-cutter performs a cutting movement relatively to the worm blankwith the transmission ratio between the worm blank and the millingcutter i=41/4.

Besides rotating around {right arrow over (k)}₁(φ₁)-axis at angularspeed {right arrow over (ω)}₁, the worm blank also makes a slight axialdisplacement along {right arrow over (k)}₁(φ₁)-axis with the valueΔk₁=1.05 mm in order to make the reference toroid of VTW worm become anelliptic or parabolic one.

While the milling cutter rotates about {right arrow over (k)}₂(φ₂)-axisat angular speed {right arrow over (ω)}₂ and simultaneously makes aradial feed along {right arrow over (i)}₂(o₂)-axis and a peripheral feedaround {right arrow over (k)}₂(φ₂)-axis.

The radius of the main basic circle of the milling cutter r_(b)=33 mmand the coordinate values of the cutting edge of the milling cutter aredescribed according to the following equationsx₂=u,y ₂ =r _(b) −v sin βz ₂ =v cos β.Where,

-   -   u=64˜74    -   v=−24˜24    -   when u=70, v=−12, then    -   x₂=70 mm,    -   y₂=33−(−12×sin 18°)=36.708 mm,    -   z₂=−12×cos 18°=−11.413 mm.        All blades are fully mounted in three dimensions on the milling        cutter body and the cutting edges are all located at a spatial        generatrix family.        Embodiment 3:

On a five-simultaneously-working-axis CNC machine-tool, given that a VTWworm to be machined has β=15.9° the inclination angle of the generatrixplane, d₁=50 mm the reference diameter, and the center distance betweenthe worm blank and the milling-cutter a=125 mm, the milling-cutterperforms a cutting movement relatively to the worm blank with thetransmission ratio between the worm blank and the milling cutter i=42/3.

Besides rotating around {right arrow over (k)}₁(φ₁)-axis at angularspeed {right arrow over (ω)}₁, the worm blank also makes a slight axialdisplacement along {right arrow over (k)}₁(φ₁)-axis with the valueΔk₁=1.1 mm in order to make the reference toroid of VTW worm become anelliptic or parabolic one.

While the milling cutter makes a slight axial displacement with thevalue Δk₂=1.3 mm along {right arrow over (k)}₂(φ₂)-axis and adifferential motion along the tangential direction around {right arrowover (k)}₂(φ₂)-axis besides rotating about {right arrow over(k)}₂(φ₂)-axis at angular speed {right arrow over (ω)}₂ andsimultaneously making a radial feed along {right arrow over(i)}₂(o₂)-axis and a peripheral feed around {right arrow over(k)}₂(φ₂)-axis. Alternatively, the feed motion of the milling cutter iscombined by three componential motions: the shift of the milling cutteralong {right arrow over (i)}₂(o₂)-axis, the shift thereof along {rightarrow over (k)}₂(φ₂)-axis and the tangential shift thereof whilerotating around {right arrow over (k)}₂(φ₂)-axis. In this case themilling cutter will completely envelop the thread of the VTW worms.

The radius of the main basic circle of the milling cutter r_(b)=38 mmand the coordinate values of the cutting edge of the milling cutter aredescribed according to the following equations:x₂=u,y ₂ =r _(b) −v sin βz ₂ =v cos β.Where,

-   -   u=80˜93    -   v=−30˜30    -   when u=90, v=15, then    -   x₂=90 mm,    -   y₂=38−15×sin 15.9°=33.891 mm,    -   z₂=15×cos 15.9°=14.426 mm.

All blades are fully mounted in three dimensions on the milling cutterbody and the cutting edges are all located at a spatial generatrixfamily.

Other preferred embodiments can be given on the basis of followingparameters: assuming that the range of the center distance a of suchworm transmissions is from 80 mm to 500 mm, the values of u, v and r_(b)can be recommended as listed in the following table.

TABLE 1 Center distance α (Unit: mm) 80 100 125 160 200 250 315 400 500μ 51~68 64~74 80~93 102~119 128~149 163~189 205~238 261~303 326~378 ν±19.4 ±24.3 ±30.4 ±38.9 ±48.6 ±60.7 ±76.5 ±97.2 ±122 r_(b)(Unit: mm)19~28 24~35 30~43 39~56 48~69 61~67  76~109  97~138 122~173 Remark: 0° ≦β ≦ 30°

Although preferred embodiments of the invention have been describedabove, this invention is not limited to the particular structures andfeatures described in detail herein. It will be apparent to thoseskilled in the art that numerous modifications form part of theinvention insofar as they do not depart from the scope of the appendedclaims.

1. A forming method for milling teeth of variable tooth worms, comprising the following steps: on a multi-axis simultaneously-working CNC machine-tool, a first moving coordinate system {σ₁(φ₁)[O₁; i₁(φ₁); j₁(φ₁), k₁(φ₁)]} is correlated to the worm blank of the VTW worms, wherein the worm blank of the VTW worms rotates around k₁(φ₁)-axis at angular speed |ω₁|; a second moving coordinate system {σ₂(φ₂)[O₂; i₂(φ₂); j₂(φ₂), k₂(φ₂)]} is correlated to the milling cutter, wherein the milling-cutter rotates around k₂(φ₂)-axis at angular speed |ω₂|, |ω₁|/|ω₂|=i₁₂ and i₁₂ is a constant; the feed motion of the milling cutter comprises the radial shift along the i₂(O₂)-axis and the peripheral shift around the k₂(φ₂)-axis; the equations of each cutting edge of the milling cutter are given as follows: x₂=u y ₂ =r _(b) −v sin β z ₂ =v cos β where, u, v are the parameters of a generatrix plane Σ of the variable tooth worms tangent to an imaginary cone; β is the inclination angle of the generatrix plane Σ relative to the axis of the imaginary cone; r_(b) is the radius of the main basic circle of the cutter body; x₂, y₂, z₂ are the coordinate values of the cutting edge on the generatrix plane, in which when the center distance between the worm blank and the milling-cutter is from 80 mm to 500 mm, the value of u is from 51 to 378, the value of v is from ±19.4 to ±122, and the value of r_(b) is from 19 mm to 173 mm; and βis greater than 0° and less than or equal to 30°; and shifting of a cutting edge of the cutter on the inclined generatrix plane in spatial locations about the milling cutter forms a cutter that will form the tooth flank of the variable tooth worms in the worm blank.
 2. The method as described in the claim 1, wherein the worm blank makes a slight axial displacement along {right arrow over (k)}₁(φ₁)-axis.
 3. The method as described in the claim 1 or claim 2, wherein the milling cutter makes both a slight displacement along axis {right arrow over (k)}₂(φ₂)-axis and a differential feeding motion along the tangential direction around {right arrow over (k)}₂(φ₂)-axis.
 4. The method as described in the claim 1, wherein when center distance between the worm blank and the milling cutter is 80 mm, the value of u is from 51 to 68, the value of v is ±19.4, and the value of r_(b) is from 19 mm to 28 mm.
 5. The method as described in the claim 1, wherein when center distance between the worm blank and the milling-cutter is 100 mm, the value of u is from 64 to 74, the value of v is ±24.3, and the value of r_(b) is from 24 mm to 35 mm.
 6. The method as described in the claim 1, wherein when center distance between the worm blank and the milling-cutter is 125 mm, the value of u is from 80 to 93, the value of v is ±30.4, and the value of r_(b) is from 30 mm to 43 mm.
 7. The method as described in the claim 1, wherein when center distance between the worm blank and the milling-cutter is 160 mm, the value of u is from 102 to 118, the value of v is ±38.9, and the value of r_(b) is from 39 mm to 56 mm.
 8. The method as described in the claim 1, wherein when center distance between the worm blank and the milling-cutter is 200 mm, the value of u is from 128 to 149, the value of v is ±48.6, and the value of r_(b) is from 48 mm to 69 mm.
 9. The method as described in the claim 1, wherein when center distance between the worm blank and the milling-cutter is 250 mm, the value of u is from 163 to 189, the value of v is ±60.7, and the value of r_(b) is from 61 mm to 87 mm.
 10. The method as described in the claim 1, wherein when center distance between the worm blank and the milling-cutter is 315 mm, the value of u is from 205 to 238, the value of v is ±76.5, and the value of r_(b) is from 76 mm to 109 mm.
 11. The method as described in the claim 1, wherein when center distance between the worm blank and the milling-cutter is 400 mm, the value of u is from 261 to 303, the value of v is ±97.2, and the value of r_(b) is from 97 mm to 138 mm.
 12. The method as described in the claim 1, wherein when center distance between the worm blank and the milling-cutter is 500 mm, the value of u is from 326 to 378, the value of v is ±122, and the value of r_(b) is from 122 mm to 173 mm. 